2D lattice-boltzmann method with detailed surface chemistry: conservation of geometrical surface

The paper discusses the coupling of detailed surface chemistry to the Lattice-Boltzmann Method and shows an
approach on how the geometrical catalytic surface can be preserved.
Results from calculations with the 2D LBM code MATRICS for formaldehyde conversion in a channel show
good agreement compared to measurements under diffusion-controlled conditions, but not for a kinetically
controlled system. Results fit for both modes of operation with results from a Finite-Volume code.
Modeling of systems with surface chemistry requires the consideration of the exact geometrical surface.
However, basis of LBM is a staircase approximation for interfaces between fluid and solid. Based on theoretical
derivations, it was shown that the asymptotic discretization error for circles is 27%. The error of skew lines is
maximal for an angle of α = 45◦ and shows the value of 41%. The discretization error for curvilinear interfaces
cannot be diminished by grid refinement.
An approach was developed, which allows the use of the exact geometric surface for calculation of surface
chemistry. It consists of two steps: 1. Implementation of the species fluxes at surfaces as volumetric sources in
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wall bounded fluid cells. 2. Segmentation of the original geometrical surface and assignment of line segments to
reactive wall cells located nearby.
The validation of the approach by calculation of flows around circles and rotated squares shows the dis-
cretization errors predicted by theory and allows to suppress the errors due to the incorporation of the exact size
of curvilinear or skew geometrical interfaces in the calculation.